Question: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-2x-6y &= -2 \\ x-9y &= -6\end{align*}$
Begin by moving the $y$ -term in the second equation to the right side of the equation. $x = {9y-6}$ Substitute this expression for $x$ in the first equation. $-2({9y - 6}) - 6y = -2$ $-18y + 12 - 6y = -2$ Simplify by combining terms, then solve for $y$ $-24y + 12 = -2$ $-24y = -14$ $y = \dfrac{7}{12}$ Substitute $\dfrac{7}{12}$ for $y$ in the top equation. $-2x-6( \dfrac{7}{12}) = -2$ $-2x-\dfrac{7}{2} = -2$ $-2x = \dfrac{3}{2}$ $x = -\dfrac{3}{4}$ The solution is $\enspace x = -\dfrac{3}{4}, \enspace y = \dfrac{7}{12}$.